Towards the prediction of flow-induced shear stress distributions experienced by breast cancer cells in the lymphatics

Abstract

Tumour metastasis in the lymphatics is a crucial step in the progression of breast cancer. The dynamics by which breast cancer cells (BCCs) travel in the lymphatics remains poorly understood. The goal of this work is to develop a model capable of predicting the shear stresses metastasising BCCs experience using numerical and experimental techniques. This paper models the fluidic transport of large particles ($\eta =d_{\mathrm{p}}/W=0.1-0.4$ where $d_{\mathrm{p}}$ is the particle diameter and W is the channel width) subjected to lymphatic flow conditions (${ Re}=0.04$), in a $100\times 100\,\upmu \hbox {m}$ microchannel. The feasibility of using the dynamic fluid body interaction (DFBI) method to predict particle motion was assessed, and particle tracking experiments were performed. The experiments found that particle translational velocity decreased from the undisturbed fluid velocity with increasing particle size (5–14% velocity lag for $\eta =0.1-0.3$). DFBI simulations were found to better predict particle behaviour than theoretical predictions; however, mesh restrictions in the near-wall region ($0.2\,\mathrm{W}>y>0.8\,\mathrm{W}$) result in computationally expensive models. The simulations were in good agreement with the experiments ($<12\%$ difference) across the channel ($0.2\,\mathrm{W}\le y\le 0.8\,\mathrm{W}$), with differences up to 25% in the near-wall region. Particles experience a range of shear stresses (0.002–0.12 Pa) and spatial shear gradients ($0.004-0.137\,\hbox {Pa}/\upmu \hbox {m}$) depending on their size and radial position. The predicted shear gradients are far in excess of values associated with BCC apoptosis ($0.004-0.023\,\hbox {Pa}/\upmu \hbox {m}$). Increasing our understanding of the shear stress magnitudes and gradients experienced by BCCs could be leveraged to elucidate whether a particular BCC size or location exists that encourages metastasis within the lymphatics.